Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
Restricted access

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Norden E. Huang

Norden E. Huang

1Laboratory for Hydrospheric Processes/Oceans and Ice Branch, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Google Scholar

Find this author on PubMed

,
Zheng Shen

Zheng Shen

Department of Earth and Planetary Sciences, The John Hopkins University, Baltimore, MD 21218, USA

Google Scholar

Find this author on PubMed

,
Steven R. Long

Steven R. Long

Laboratory for Hydrospheric Processes/Observational Science Branch, NASA Wallops Flight Facility, Wallops Island, VA 23337, USA

Google Scholar

Find this author on PubMed

,
Manli C. Wu

Manli C. Wu

Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Google Scholar

Find this author on PubMed

,
Hsing H. Shih

Hsing H. Shih

NOAA National Ocean Service, Silver Spring, MD 20910, USA

Google Scholar

Find this author on PubMed

,
Quanan Zheng

Quanan Zheng

College of Marine Studies, University of Delaware, DE 19716, USA

Google Scholar

Find this author on PubMed

,
Nai-Chyuan Yen

Nai-Chyuan Yen

Naval Research Laboratory, Washington, DC, 20375–5000, USA

Google Scholar

Find this author on PubMed

,
Chi Chao Tung

Chi Chao Tung

8Department of Civil Engineering, North Carolina State University, Raleigh, NC 27695–7908, USA

Google Scholar

Find this author on PubMed

and
Henry H. Liu

Henry H. Liu

9Naval Surface Warfare Center, Carderock Division, Bethesda, MD 20084–5000, USA

Google Scholar

Find this author on PubMed

    A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the ‘empirical mode decomposition’ method with which any complicated data set can be decomposed into a finite and often small number of ‘intrinsic mode functions’ that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the ‘instrinic mode functions’ yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of ‘intrinsic mode functions’ based on local properties of the signal, which make the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and non-stationary effects in the energy-frequency-time distribution.